This OpenLog has on-board low drop regulator (MIC5205-3.3) and works from 3.3 up to 12Volts. Recommended 3.3-5Volt obviously for power dissipation reasons. So power is no problem to be connected to 5Volts.

But do not know if the ATMEGA328 is tolerant on 5volt at the pins having 3.3 volts on power supply.

Ioannis